Finite Math Examples

$2 x - 4 = 7 x - \frac{3}{5}$

Step 1

Move all terms containing $x$ to the left side of the equation.

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Step 1.1

Subtract $7 x$ from both sides of the equation.

$2 x - 4 - 7 x = - \frac{3}{5}$

Step 1.2

Subtract $7 x$ from $2 x$ .

$- 5 x - 4 = - \frac{3}{5}$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $4$ to both sides of the equation.

$- 5 x = - \frac{3}{5} + 4$

Step 2.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 5 x = - \frac{3}{5} + 4 \cdot \frac{5}{5}$

Step 2.3

Combine $4$ and $\frac{5}{5}$ .

$- 5 x = - \frac{3}{5} + \frac{4 \cdot 5}{5}$

Step 2.4

Combine the numerators over the common denominator.

$- 5 x = \frac{- 3 + 4 \cdot 5}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $5$ .

$- 5 x = \frac{- 3 + 20}{5}$

Step 2.5.2

Add $- 3$ and $20$ .

$- 5 x = \frac{17}{5}$

Step 3

Divide each term in $- 5 x = \frac{17}{5}$ by $- 5$ and simplify.

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Step 3.1

Divide each term in $- 5 x = \frac{17}{5}$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{\frac{17}{5}}{- 5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{\frac{17}{5}}{- 5}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{17}{5}}{- 5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{17}{5} \cdot \frac{1}{- 5}$

Step 3.3.2

Move the negative in front of the fraction.

$x = \frac{17}{5} (- \frac{1}{5})$

Step 3.3.3

Multiply $\frac{17}{5} (- \frac{1}{5})$ .

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Step 3.3.3.1

Multiply $\frac{17}{5}$ by $\frac{1}{5}$ .

$x = - \frac{17}{5 \cdot 5}$

Step 3.3.3.2

Multiply $5$ by $5$ .

$x = - \frac{17}{25}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{17}{25}$

Decimal Form:

$x = - 0.68$